Domb-Joyce模型和Go模型的多规范模拟：自避免行走的新枚举方法
Multicanonical simulation of the Domb-Joyce model and the Go model: new enumeration methods for self-avoiding walks
摘要：
我们开发的统计枚举方法，使用一个强大的抽样技术，称为multicanonical蒙特卡罗方法的自我避免散步。利用这些方法，我们估计了二维N步自回避行走的数目N=256，具有统计误差。所开发的方法是基于统计力学模型的路径，其中包括自我避免步行。用于选择用于枚举自避免行走的合适的模型的标准是该模型的配置空间是否包括元素的数目可以被精确计数的集合。我们称这个集合为刻度固定集合。我们选择了以下两个模型，满足标准：格点蛋白质的Go模型和广义随机游动的Domb-Joyce模型。这两种模型在位形空间的结构上存在着差异。Go模型的位形空间被定义为自回避游动的泛集，而基态构象的集合提供了一个标度固定集。另一方面，Domb-Joyce模型的构型空间被定义为随机游动的泛集，它可以作为标度固定集，而基态构象的集合与自回避游动的泛集相同.从枚举性能的角度来看，我们得出结论，Domb-Joyce模型是更好的两个。性能差异的原因部分地由Go模型的一阶相变的存在来解释。
英文摘要：
We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding walks up to N=256 with statistical errors. The developed methods are based on statistical mechanical models of paths which include self-avoiding walks. The criterion for selecting a suitable model for enumerating self-avoiding walks is whether or not the configuration space of the model includes a set for which the number of the elements can be exactly counted. We call this set a scale fixing set. We selected the following two models which satisfy the criterion: the Go model for lattice proteins and the Domb-Joyce model for generalized random walks. There is a contrast between these two models in the structures of the configuration space. The configuration space of the Go model is defined as the universal set of self-avoiding walks, and the set of the ground state conformation provides a scale fixing set. On the other hand, the configuration space of the Domb-Joyce model is defined as the universal set of random walks which can be used as a scale fixing set, and the set of the ground state conformation is the same as the universal set of self-avoiding walks. From the perspective of enumeration performance, we conclude that the Domb-Joyce model is the better of the two. The reason for the performance difference is partly explained by the existence of the first-order phase transition of the Go model.
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